Chapter 5: Time value of money
One Period Case
Dollar today is worth more than a dollar in the future because....
People prefer present consumption over future
Monetary inflation
Uncertainty with future cash flows reduces value
FV = C0 x (1 + r)
PV = C1 / (1 + r)
Value of financial securities
To value bonds and stocks you need to...
Estimate future cash flows
- Size (how much)
- Timing (when)
- Discount CF at appropriate rate
Corporate debt
short or long term and can be public issued or privately placed
Different from shares:
-creditos claim on corporation is specified
-promised cash flows
-Many are callable
Direct placement compared to public issues
Difference between direct private long term financing and public issues of debt are:
1. Registration costs are lower for direct financing
2. Direct financing is likely to have more restrictive covenants
3. It is easier to renegotiate a term loan or a private placement in the event of default
4. Life insurance companies and pension funds predominate the private placement market. Chartered banks participate predominantly in the term market
5. Cost of distributing loans in the private market is less due to smaller number of buyers and no underwriter required
Multi Period Case
Future value of an investment over many periods
FV = C0 x (1 + r)^T
PV = FV / (1 + r)^T
Coupon:
Face Value:
Bonds: A debt instrument issued by a corporation or government to raise large amounts of long term capital
In return for the use of borrowed funds, the borrowers promise to make payments of principal and interest on specified date
Coupon: The stated interest on the bond
Face Value: The denomination of each individual bond
1 Features of a typical bond
2 Features that may change
1 Amount of issue, date of issue, maturity
-face value
-annual coupon, dates of coupon pmts
-security
-sinking funds
-call provisions
-covenants
2 Rating
YTM
Market price
Mortgage question calculation
Find the following terms:
r = rate which you switch to EPR, EAR, and back to EPR
PV = Principal, how much is owing after down payment
PMT = monthly pmts might be given or need to be found using financial calculator
Use PV of an annuity formula or financial calculator
Terms:
Perpetuity:
Growing Perpetuity:
Annuity:
Growing Annuity:
Perpetuity: Stream of constant cash flows that lasts forever - PV = C / r
Growing Perpetuity: A stream of cash flows that grows at a constant rate forever - PV = C / (r - g)
Annuity: Stream of constant cash flows that lasts for a fixed number of periods - PV = (PMT / r)(1 - 1/(1 + r)^t) and FV = PMT x (1 / r )((1 + r)^T) - 1
Growing Annuity: Stream of cash flows that grows at a constant rate for a fixed number of periods
FV = P ((1 + r)^n) - (1 + g)^n) / (r - g))
PV = (C / r - g)(1 - (1 + g / 1 + r)^n)
Terms
Maturity date:
Time to maturity:
Quoted yield:
Yield to maturity:
Maturity date: the date for any final payment of a bond
Time to maturity: maturity date (T) -todays date (t)
Quoted yield: stated annual rate (r) which should be converted into (EPR) in bonds valuation
Yield to maturity: discount rate that equates the PV of interest payments and face value with PV of the bond
Value determined by PV, Coupon pmts, and par value
Security:
Seniority:
Protective covenants:
Sinking fund:
Call provision:
Security: Collateral - assets are pledged as security for pmt of debt, protects bond holder incase on non-payment, mortgage securities are secured by real estate or long term assets, value depends on value of underlying security, debentures are unsecured bonds with no specific pledge of security
Seniority: Indicates preference in position over other lenders, junior or subordinated debt would "rank" behind the senior bondholders and be settled after the senior creditors are compensated
Protective covenants: Agreements to protect bondholders, negative covenants - thou shalt not - pay dividends above specified amount, pledge assets to other lenders, sell more senior debt or issue new debt, sell or lease assets without lender approval, merge with another firm. Positive covenant thou shalt - maintain working capital at a minimal level, use proceeds from sale of assets for other assets, allow redemption in event of merger or spinoff, maintain good condition of assets, provide audited financial info.
Sinking fund: start between 5 -10 years after initial issuance, some establish equal pmts over the life of the bond, most high quality bond issues establish pmts to the sinking fund that are not sufficient to redeem the entire issue. Sinking funds provide extra protection to bondholders and provide the firm with an option if prices fall below par the firm buys back bonds at the lower market price and if prices rise above par firms buy back at lower face value
Call provision: allows the company to repurchase or call the entire bond issue at a predetermined price over a specified period - call and price and face value is call premium difference. Call works to the advantage of the issuer if interest rates fall and bond prices rise the option too buy back bonds at call price is valuable, bondholders demand higher interest rates on callable bonds, any expected gains to issuer from being allowed to refund the bond will be offset by higher initial interest rates
Calculate opportunity costs
Add up every little cost that comes from renting including the down payment also
Different Rates
Stated annual interest rate (r):
Effective Period Interest Rate (EPR):
Effective Annual Interest Rate (EAR):
r - simple percentage interest changed during a year
EPR - Actual percentage interest charged per period
EAR - Actual percentage interest (simple and compounded) charged over a year
Types of bonds
Pure discount bonds:
Coupon bonds:
Consols:
Pure discount bonds: No periodic interest payments (coupon rate = 0%), YTM comes from difference in purchase price and par value, cannot sell more than par, called zeroes, original issue discount, (principal-only) T-bills. PV = F / (1 + r)^T
Coupon bonds: Make periodic coupon payments in addition to maturity value, pmts are equal each period. Therefore, the bond is just a combination of an annuity and a terminal value and they are typically semiannual PV = C / r (1 - 1 / (1 + r)^T) + F / (1 + r)^T
Consols: Not all bonds have a final maturity, British console pay a set amount every period forever, literally a perpetuity. PV = C / r
Bond ratings:
Junk bonds:
Bond ratings: likelihood the firm will default, protection afforded by loan contract in event of default
Firms pay to have bonds rated are constructed from financial statements supplied by firm, ratings can change and disagree
Investment grade
Moody (Aa3, A1, A2) S&P's (AA-, A+, A) Upper-medium quality investment grade bonds
Junk Bonds: anything less than S&P "BB" or a moody's "Ba" is a junk bond. 2 types go issue junk - possibly not rates and fallen angels - rated. Junk is high yield bond or low grade, used for restructurings, mergers, and going private
Calculate cost of buying
down payment amount + all taxes + any fees x rate calculated using (r - EPR - EAR - EPR)
Canadian Mortgages
They quote the annual interest compounded semi-annually for mortgages, although interest is calculated (compounded) every month
Bond Concepts
Bond prices and market interest rates move in opposite directions
When coupon rate = quoted yield the price = par value (bond sells at par)
when coupon rate > quoted yield the price > par value (bond sells at a premium)
When coupon rate < quoted yield the price < par value (bond sells at a discount)
High coupon rate high bond price and high yield means low bond price
Different types of bonds
Floating rate bonds:
Direct placement compared to public issues:
Long-term syndicated bank loans:
Floating rate bonds:coupon payments are adjustable. Tied to T-bill rate or another short-term interest rate. Majority of floaters have the following - put provision, coupon rate has a floor and a ceiling
Direct placement compared to public issues: 2 forms one being term loans - maturities up to 5 years and two private placements - maturities longer than 5 years
Long-term syndicated bank loans: corporate loan made by a group of banks and other institutional investors, can be publicly traded, may be a line of credit and be "undrawn" or it may be drawn and used by a firm, are always rate investment grade, leveraged syndicated loan is junk
Calculate mortgage payments after a certain time period has lapsed
Literally the exact same thing once you have r, PV, and N all you do is multiply the amount of years by m and subtract it by the total amount
ex. a 25 year mortgage wondering how much is left after 5 years - (5 x 12 = 60 and then do 300 - 60 = 240) so 240 would be the new N instead of 300